A Biology Professor Responds to Some Student Questions by E-Mail

Essay

A biology professor responds to some student questions by e-mail. The probability model
below describes the number of e-mails that the professor may receive from students
during a day. $$\begin{array} { l | c | c | c | c | c | c } \text { e-mails received } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Probability } & 0.05 & 0.10 & 0.20 & 0.25 & 0.30 & 0.10\end{array}$$
a. How many e-mails should the professor expect to receive each day?
b. What is the standard deviation?
c. If it takes the professor an average of ten minutes to respond to each e-mail, how much
time should the professor expect to spend responding to student e-mails each day?